# Group in which every normal subgroup is finite or has finite index

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

## Definition

A group in which every normal subgroup is finite or has finite index is a group in which every normal subgroup satisfies one of these two conditions: either it is a finite group (and hence a finite normal subgroup), or it is a normal subgroup of finite index in the whole group.

## Relation with other properties

### Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
simple group
finite group
group in which every nontrivial normal subgroup has finite index